<p>I am a student who is about to start his freshman year. I really want to major in mathematics and then get a PhD in it and become an academician.
Can any math students post about how you do research in math as an undergraduate? This question can sound very naive but I still want to ask: There are many REUs during summers and most of them give you stipends. Not that I am against receiving money, but why does someone who is doing research in math need money? I mean you don't need a lab with lots of different equipment like bio majors. Do you need anything other than pen, paper and a creative smart mind?</p>
<p>REUs offer a stipend to assist with living and housing expenses, since they often do not allow you to have any outside work during the program. They are not giving you money to buy equipment–you would generally use whatever equipment the person/lab you are working with has access to.</p>
<p>A lot of math research involves some pretty extensive computer setups, because some equations can’t be solved by a person in anything resembling a reasonable amount of time. But, as mentioned, the stipend isn’t meant for research costs. It’s meant as a wage to cover living expenses.</p>
<p>The stipends for undergrad internships/research opportunities are usually quite generous. Aside from covering living expenses, you can usually manage to squirrel away a decent amount of it for future school expenses.</p>
<p>Thanks everyone! I understand the stipend thing now. Had just one more question: how early can you start doing research in math with a professor in your university? I will be done with multivariable calculus and intro to theoretical math (proof writing/reading course) by the end of my freshman year. I fear of approaching to a professor to ask if I can join to his/her research because I am more afraid that he/she will say: “what the hell you know?”</p>
<p>Researchers get a salary or stipend which is distinct from money they get for research. “Research grants” they receive get a one-third chunk taken out for their university. Or something like that. And their salary comes from the university, not grants DIRECTLY.</p>
<p>As a Math major, I did not go the research route. I was strictly an “applied” guy, but at least I can give you insight on your course selection. You probably have to follow the “pure” math emphasis because that is what graduate math programs will look for.</p>
<p>Where some of the more applied Math majors have the option of taking one semester of either Real Analysis or Abstract Algebra, you will have to take the full year of both topics.</p>
<p>If I took those two year long sequences with an applied math major would I then be as qualified for grad school in math as a pure math major? Also, does the pure math major being more qualified only apply to math grad school or would it also work with other grad school choices…econ, cs, engineering, etc.?</p>
<p>Globaltraveler is incorrect. Pure math does not better qualify you for “grad school”, it better qualifies you for pure math grad school. Applied math better prepares you for applied math grad school as well as other fields like cs, engineering, physics. If anything, the applied math major is more broadly “qualified”.</p>
<p>robcol - First and foremost, there is absolutely no harm in asking (even as a freshman). I personally know quite a few people (including myself) who did/are doing math research with their professors immediately after their freshman year. In all of the above cases, the professors were more than willing to work with the students in question.</p>
<p>On the other hand… to be honest, it would (generally) be better if you had more background than that to be doing research. The work is, after all, quite advanced. All of the people I know involved in research have had at least some working knowledge of algebra as well as real and complex analysis (because even seemingly unrelated areas of math tend to rely on basic knowledge of all of the above). Personally, I would probably wait a year, because I wouldn’t want to be overwhelmed.</p>
<p>However, that shouldn’t stop you from trying if you feel you’ll be okay. Look at your professors’ web sites and try to skim through some of their work (don’t expect to fully understand it or feel discouraged if you don’t). If you think you could realistically pick up the background as you go, then go for it.</p>
<p>Also - I’m sure the faculty at your school will give you advice (if you ask) on what they think is best in your situation.</p>
<p>I’d also like to know what evidence/reasoning jbrussell has for his claim that applied math better prepares you for grad school in Physics or CS - as far as I can tell, this is going to be very dependent on exactly what Physics or CS you’re planning on doing.</p>
<p>I was speaking from a “required courses” point of view. True, it really doesn’t matter how one names their math degree, but to do a MS–>PhD plan, one will need full year sequences of BOTH Algebra and Analysis (real or advanced calculus), while most applied plans only require one semester of one or the other (usually analysis).</p>
<p>Anyone can call there math specialty whatever they want.</p>
I disagree. Pure math is a better preparation for applied math grad school than the typical applied math major. Turns out that the pure math concepts developed 100 years ago - the typical 1st year PhD curriculum in pure math - are essential for most modern approaches to applied math as well. </p>
<p>Cryptography relies on algebra, signal processing on functional analysis and probability theory on measure theory. </p>
<p>An applied math major who doesn’t take the standard upper-level pure math courses will be woefully underprepared for the graduate-level work in pure math that’s necessary to make a meaningful contribution to the theory of applied mathematics.</p>